We consider the massive neutrino model called the Type-I seesaw [1]}, [2]}, [3]}, [4]}, [5]} first with two right-handed neutrinos, the 3-2 seesaw model; then with three right-handed neutrinos, the 3-3 seesaw modelA model with only one right-handed fermion is excluded by the measured mass squared differences of oscillation experiments..
For the 3-2 seesaw model the neutrino Dirac mass matrix is a 3 by 2 matrix and its rank is two.
The 3-2 seesaw model has been previously studied sometimes under the name the minimal Type-I seesaw model [6]}, [7]}, [8]}, [9]}, [10]}, [11]}, [12]}, [13]}.
For the model with three right-handed neutrinos, we assume a texture of the neutrino Dirac mass terms to reduce the rank of the matrix to two.
Both of those models lead to a vanishing mass for the lightest neutrino, i.e., \(m_1=0\)  for normal hierarchy.
In the usual Type-I seesaw the right-handed neutrinos have a significantly heavier mass than the Standard Model particle content to reproduce small neutrino masses.
This means the heavy right-handed neutrinos are integrated out at low-energy scalesDifferent nomenclature is used in literature to name the heavy right-handed neutrinos, for example right-handed neutrinos or heavy neutrino singlets or simply heavy neutrinos.
